{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- TODO: Self-organizing maps and hexagonal grids (Kohonen 1982; Huysmans et al.  2006a; Seret et al. 2012). A SOM -->\n",
    "<!-- TODO: DBScan, TSNE, <https://speakerdeck.com/lmcinnes/umap-uniform-manifold-approximation-and-projection-for-dimension-reduction> -->\n",
    "<!-- TODO: Good overview and connections to optimization <https://www.youtube.com/watch>?time_continue=1&v=9iol3Lk6kyU -->\n",
    "<!-- TODO:    - Generalized_low_rank_models_Udell -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "image/png": {
       "width": 200
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image('../../Python_probability_statistics_machine_learning_2E.png',width=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from matplotlib.pylab import subplots\n",
    "import numpy as np\n",
    "from sklearn.datasets import make_blobs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clustering is the simplest member of a family of machine learning methods that\n",
    "do not require supervision to learn from data. Unsupervised methods\n",
    "have training sets that do not have a target variable. These unsupervised learning\n",
    "methods rely upon a meaningful metric to group data into \n",
    "clusters. This makes it an excellent exploratory data analysis\n",
    "method because there are very few assumptions built into the method itself.\n",
    "In this section, we focus on the popular K-means clustering method that is\n",
    "available in Scikit-learn.\n",
    "\n",
    "Let's manufacture some data to get going with `make_blobs` from Scikit-learn.\n",
    "[Figure](#fig:clustering_001) shows some example clusters in two dimensions.\n",
    "Clustering methods work by minimizing the following objective function,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "fig,ax=subplots()\n",
    "X, y = make_blobs(n_samples=300, centers=5,\n",
    "                  random_state=0, cluster_std=0.5)\n",
    "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='cool',alpha=.8);\n",
    "_=ax.set_xlabel('x-coordinate',fontsize=16)\n",
    "_=ax.set_ylabel('y-coordinate',fontsize=16)\n",
    "_=ax.axis(xmax=4,ymin=-2)\n",
    "ax.tick_params(labelsize='x-large')\n",
    "ax.set_aspect(1/1.6)\n",
    "fig.savefig('fig-machine_learning/clustering_001.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/clustering_001.png, width=500 frac=0.85]  The four clusters are pretty easy to see in this example and we want clustering methods to determine the extent and number of such clusters automatically.  <div id=\"fig:clustering_001\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:clustering_001\"></div>\n",
    "\n",
    "<p>The four clusters are pretty easy to see in this example and we want clustering methods to determine the extent and number of such clusters automatically.</p>\n",
    "<img src=\"fig-machine_learning/clustering_001.png\" width=300>\n",
    "\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "J = \\sum_k \\sum_i \\Vert \\mathbf{x}_i-\\mathbf{\\mu}_k \\Vert^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The *distortion* for the $k^{th}$ cluster is the summand,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_i \\Vert \\mathbf{x}_i - \\mathbf{ \\mu }_k \\Vert^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Thus, clustering algorithms work to minimize this by adjusting the\n",
    "centers of the individual clusters, $\\mu_k$. Intuitively, each $\\mu_k$ is the\n",
    "*center of mass* of the points in the cloud.  The Euclidean distance is\n",
    "the typical metric used for this,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\Vert \\mathbf{ x } \\Vert^2 = \\sum x_i^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " There are many clever algorithms that can solve this problem for\n",
    "the best $\\mu_k$ cluster-centers. The K-means algorithm starts with a\n",
    "user-specified number of $K$ clusters to optimize over.  This is implemented in\n",
    "Scikit-learn with the `KMeans` object that follows the usual fitting\n",
    "conventions in Scikit-learn,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "       n_clusters=4, n_init=10, n_jobs=None, precompute_distances='auto',\n",
       "       random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(n_clusters=4)\n",
    "kmeans.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " where we  have chosen $K=4$. How do we choose the value of\n",
    "$K$?  This is the eternal question of generalization versus\n",
    "approximation --- too many clusters provide great approximation but\n",
    "bad generalization. One way to approach this problem is to compute the\n",
    "mean distortion for increasingly larger values of $K$ until it no\n",
    "longer makes sense. To do this, we want to take every data point and\n",
    "compare it to the centers of all the clusters.  Then, take the\n",
    "smallest value of this across all clusters and average those. This\n",
    "gives us an idea of the overall mean performance for the $K$ clusters.\n",
    "The following code computes this explicitly.\n",
    "\n",
    "**Programming Tip.**\n",
    "\n",
    "The `cdist` function from Scipy computes all the pairwise\n",
    "differences between the two input collections according to the\n",
    "specified metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import cdist\n",
    "m_distortions=[]\n",
    "for k in range(1,7):\n",
    "    kmeans = KMeans(n_clusters=k)\n",
    "    _=kmeans.fit(X)\n",
    "    tmp=cdist(X,kmeans.cluster_centers_,'euclidean')\n",
    "    m_distortions.append(sum(np.min(tmp,axis=1))/X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=subplots()\n",
    "fig.set_size_inches((8,5))\n",
    "_=ax.plot(m_distortions,'-o',ms=10,color='gray')\n",
    "_=ax.set_xlabel('K',fontsize=16)\n",
    "_=ax.set_ylabel('Mean Distortion',fontsize=16)\n",
    "ax.tick_params(labelsize='x-large')\n",
    "# ax.set_aspect(1/1.6)\n",
    "fig.savefig('fig-machine_learning/clustering_002.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/clustering_002.png, width=500 frac=0.75] The Mean Distortion shows that there is a diminishing value in using more clusters.  <div id=\"fig:clustering_002\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:clustering_002\"></div>\n",
    "\n",
    "<p>The Mean Distortion shows that there is a diminishing value in using more clusters.</p>\n",
    "<img src=\"fig-machine_learning/clustering_002.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    " Note that code above uses the `cluster_centers_`, which are\n",
    "estimated from K-means algorithm. The resulting [Figure](#fig:clustering_002) shows the point of diminishing returns for\n",
    "added additional clusters.\n",
    "\n",
    "\n",
    "Another figure-of-merit is the silhouette coefficient, which measures\n",
    "how compact and separated the individual clusters are. To  compute the\n",
    "silhouette coefficient, we need to compute the mean intra-cluster\n",
    "distance for each sample ($a_i$) and the mean distance to the next\n",
    "nearest cluster ($b_i$). Then, the silhouette coefficient for the\n",
    "$i^{th}$ sample is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\texttt{sc}_i = \\frac{b_i-a_i}{\\max(a_i,b_i)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The mean silhouette coefficient is just the mean of all these values\n",
    "over all the samples.  The best value is one and the worst is negative one,\n",
    "with values near zero indicating overlapping clusters and negative values\n",
    "showing that samples have been incorrectly assigned to the wrong cluster.  This\n",
    "figure-of-merit is implemented in Scikit-learn as in the following,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def scatter_fit(X,y,ax):\n",
    "    _=kmeans.fit(X)\n",
    "    _=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='.')\n",
    "    _=ax.set_title('silhouette={:.3f}'.format(silhouette_score(X,kmeans.labels_)))\n",
    "\n",
    "fig,axs = subplots(2,2,sharex=True,sharey=True)\n",
    "np.random.seed(12)\n",
    "ax=axs[0,0]\n",
    "X,y=make_blobs(centers=[[0,0],[3,0]],n_samples=100)\n",
    "scatter_fit(X,y,ax)\n",
    "ax=axs[0,1]\n",
    "X,y=make_blobs(centers=[[0,0],[10,0]],n_samples=100)\n",
    "scatter_fit(X,y,ax)\n",
    "ax=axs[1,0]\n",
    "X,y=make_blobs(centers=[[0,0],[3,0]],n_samples=100,cluster_std=[.5,.5])\n",
    "scatter_fit(X,y,ax)\n",
    "ax=axs[1,1]\n",
    "X,y=make_blobs(centers=[[0,0],[10,0]],n_samples=100,cluster_std=[.5,.5])\n",
    "scatter_fit(X,y,ax)\n",
    "fig.savefig('fig-machine_learning/clustering_003.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " [Figure](#fig:clustering_004) shows how the silhouette coefficient varies\n",
    "as the clusters become more dispersed and/or closer together.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-machine_learning/clustering_003.png, width=500 frac=0.85]  The shows how the silhouette coefficient varies as the clusters move closer and become more compact. <div id=\"fig:clustering_003\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:clustering_003\"></div>\n",
    "\n",
    "<p>The shows how the silhouette coefficient varies as the clusters move closer and become more compact.</p>\n",
    "<img src=\"fig-machine_learning/clustering_003.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "K-means is easy to understand  and to implement, but can be sensitive\n",
    "to the initial choice of cluster-centers. The default initialization\n",
    "method in Scikit-learn uses a very effective and clever randomization\n",
    "to come up with the initial cluster-centers. Nonetheless, to see why\n",
    "initialization can cause instability with K-means, consider the\n",
    "following [Figure](#fig:clustering_004), In [Figure](#fig:clustering_004), there are two large clusters on the left and\n",
    "a very sparse cluster on the far right. The large circles at the\n",
    "centers are the cluster-centers that K-means found. Given $K=2$, how\n",
    "should the cluster-centers be chosen? Intuitively, the first two\n",
    "clusters should have their own cluster-center somewhere between them\n",
    "and the sparse cluster on the right should have its own cluster-center [^kmeans].  \n",
    "Why isn't this happening?\n",
    "\n",
    "[^kmeans]: Note that we are using the `init=random` keyword argument for this\n",
    "example in order to illustrate this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,y = make_blobs(centers=[[0,0],[5,0]],random_state=100,n_samples=200)\n",
    "Xx,yx=make_blobs(centers=[[20,0]],random_state=100,n_samples=3)\n",
    "X=np.vstack([X,Xx])\n",
    "y=np.hstack([y,yx+2])\n",
    "\n",
    "fig,axs=subplots(2,1,sharex=True,sharey=True)\n",
    "ax=axs[0]\n",
    "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='.',alpha=.3);\n",
    "_=kmeans = KMeans(n_clusters=2,random_state=123,init='random')\n",
    "_=kmeans.fit(X)\n",
    "_=ax.set_aspect(1)\n",
    "_=ax.plot(kmeans.cluster_centers_[:,0],kmeans.cluster_centers_[:,1],'o',color='gray',ms=15,alpha=.5)\n",
    "\n",
    "X,y = make_blobs(centers=[[0,0],[5,0]],random_state=100,n_samples=200)\n",
    "Xx,yx=make_blobs(centers=[[20,0]],random_state=100,n_samples=10)\n",
    "X=np.vstack([X,Xx])\n",
    "y=np.hstack([y,yx+2])\n",
    "\n",
    "ax=axs[1]\n",
    "_=ax.scatter(X[:,0],X[:,1],c=y,s=50,cmap='gray',marker='.',alpha=.3);\n",
    "kmeans = KMeans(n_clusters=2,random_state=123,init='random')\n",
    "_=kmeans.fit(X)\n",
    "_=ax.set_aspect(1)\n",
    "_=ax.plot(kmeans.cluster_centers_[:,0],kmeans.cluster_centers_[:,1],'o',color='gray',ms=15,alpha=.8)\n",
    "fig.savefig('fig-machine_learning/clustering_004.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- dom:FIGURE: [fig-machine_learning/clustering_004.png, width=500 frac=0.85]  The large circles indicate the cluster-centers found by the K-means algorithm. <div id=\"fig:clustering_004\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:clustering_004\"></div>\n",
    "\n",
    "<p>The large circles indicate the cluster-centers found by the K-means algorithm.</p>\n",
    "<img src=\"fig-machine_learning/clustering_004.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "The problem is that the objective function for K-means is trading the distance\n",
    "of the far-off sparse cluster with its small size. If we keep increasing the\n",
    "number of samples in the sparse cluster on the right, then K-means will move\n",
    "the cluster centers out to meet them,  as shown in [Figure](#fig:clustering_004). That is, if one of the initial cluster-centers was\n",
    "right in the middle of the sparse cluster, the the algorithm would have\n",
    "immediately captured it and then moved the next cluster-center to the middle of\n",
    "the other two clusters (bottom panel of [Figure](#fig:clustering_004)).\n",
    "Without some thoughtful initialization, this may not happen and the sparse\n",
    "cluster would have been merged into the middle cluster (top panel of [Figure](#fig:clustering_004)). Furthermore, such problems are hard to visualize with\n",
    "high-dimensional clusters. Nonetheless, K-means is generally very fast,\n",
    "easy-to-interpret, and easy to understand. It is straightforward to parallelize\n",
    "using the `n_jobs` keyword argument so that many initial cluster-centers can be\n",
    "easily evaluated.  Many extensions of K-means use different metrics beyond\n",
    "Euclidean  and incorporate adaptive weighting of features. This enables the\n",
    "clusters to have ellipsoidal instead of spherical shapes."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "pygments_lexer": "ipython3",
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